In this paper, the minimum spanning tree problem is investigated on the graph with fuzzy edge weights. The notion of fuzzy $\mathit{\alpha }$-minimum spanning tree is presented based on the credibility measure, and then the solutions of the fuzzy $\mathit{\alpha }$-minimum spanning tree problem are discussed under different assumptions. First, we respectively, assume that all the edge weights are triangular fuzzy numbers and trapezoidal fuzzy numbers and prove that the fuzzy $\mathit{\alpha }$-minimum spanning tree problem can be transformed to a classical problem on a crisp graph in these two cases, which can be solved by classical algorithms such as the Kruskal algorithm and the Prim algorithm in polynomial time. Subsequently, as for the case that the edge weights are general fuzzy numbers, a fuzzy simulation-based genetic algorithm using Prüfer number representation is designed for solving the fuzzy $\mathit{\alpha }$-minimum spanning tree problem. Some numerical examples are also provided for illustrating the effectiveness of the proposed solutions.

The USDA National Agricultural Statistics Service (NASS) and other federal statistical agencies have used probability-based surveys as the foundation for official statistics for over half a century. Non-survey data that can be used to improve the accuracy and precision of estimates such as administrative, remotely sensed, and retail data have become increasingly available. Both frequentist and Bayesian models are used to combine survey and non-survey data in a principled manner. NASS has recently adopted Bayesian subarea models for three of its national programs: farm labor, crop county estimates, and cash rent county estimates. Each program provides valuable estimates at multiple scales of geography. For each program, technical challenges had to be met and a strenuous review completed before models could be adopted as the foundation for official statistics. Moving models out of the research phase into production required major changes in the production process and a cultural shift. With the implemented models, NASS now has measures of uncertainty, transparency, and reproducibility of its official statistics.

In the production of US agricultural official statistics, certain inequality and benchmarking constraints must be satisfied. For example, available administrative data provide an accurate lower bound for the county-level estimates of planted acres, produced by the U.S. Department of Agriculture’s (USDA) National Agricultural statistics Services (NASS). In addition, the county-level estimates within a state need to add to the state-level estimates. A sub-area hierarchical Bayesian model with inequality constraints to produce county-level estimates that satisfy these important relationships is discussed, along with associated measures of uncertainty. This model combines the County Agricultural Production Survey (CAPS) data with administrative data. Inequality constraints add complexity to fitting the model and present a computational challenge to a full Bayesian approach. To evaluate the inclusion of these constraints, the models with and without inequality constraints were compared using 2014 corn planted acres estimates for three states. The performance of the model with inequality constraints illustrates the improvement of county-level estimates in accuracy and precision while preserving required relationships.

The presence of outliers in a dataset can substantially bias the results of statistical analyses. In general, micro edits are often performed manually on all records to correct for outliers. A set of constraints and decision rules is used to simplify the editing process. However, agricultural data collected through repeated surveys are characterized by complex relationships that make revision and vetting challenging. Therefore, maintaining high data-quality standards is not sustainable in short timeframes. The United States Department of Agriculture’s (USDA’s) National Agricultural Statistics Service (NASS) has partially automated its editing process to improve the accuracy of final estimates. NASS has investigated several methods to modernize its anomaly detection system because simple decision rules may not detect anomalies that break linear relationships. In this article, a computationally efficient method that identifies format-inconsistent, historical, tail, and relational anomalies at the data-entry level is introduced. Four separate scores (i.e., one for each anomaly type) are computed for all nonmissing values in a dataset. A distribution-free method motivated by the Bienaymé-Chebyshev’s inequality is used for scoring the data entries. Fuzzy logic is then considered for combining four individual scores into one final score to determine the outliers. The performance of the proposed approach is illustrated with an application to NASS survey data.

The use of hierarchical Bayesian small area models, which take survey estimates along with auxiliary data as input to produce official statistics, has increased in recent years. Survey estimates for small domains are usually unreliable due to small sample sizes, and the corresponding sampling variances can also be imprecise and unreliable. This affects the performance of the model (i.e., the model will not produce an estimate or will produce a low-quality modeled estimate), which results in a reduced number of official statistics published by a government agency. To mitigate the unreliable sampling variances, these survey-estimated variances are typically modeled against the direct estimates wherever a relationship between the two is present. However, this is not always the case. This paper explores different alternatives to mitigate the unreliable (beyond some threshold) sampling variances. A Bayesian approach under the area-level model set-up and a distribution-free technique based on bootstrap sampling are proposed to update the survey data. An application to the county-level corn yield data from the County Agricultural Production Survey of the United States Department of Agriculture’s (USDA’s) National Agricultural Statistics Service (NASS) is used to illustrate the proposed approaches. The final county-level model-based estimates for small area domains, produced based on updated survey data from each method, are compared with county-level model-based estimates produced based on the original survey data and the official statistics published in 2016.

The United States Department of Agriculture’s (USDA’s) National Agricultural Statistics Service (NASS) conducts the Farm Labor Survey to produce estimates of the number of workers, duration of the workweek, and wage rates for all agricultural workers. Traditionally, expert opinion is used to integrate auxiliary information, such as the previous year’s estimates, with the survey’s direct estimates. Alternatively, implementing small area models for integrating survey estimates with additional sources of information provides more reliable official estimates and valid measures of uncertainty for each type of estimate. In this paper, several hierarchical Bayesian subarea-level models are developed in support of different estimates of interest in the Farm Labor Survey. A 2020 case study illustrates the improvement of the direct survey estimates for areas with small sample sizes by using auxiliary information and borrowing information across areas and subareas. The resulting framework provides a complete set of coherent estimates for all required geographic levels. These methods were incorporated into the official Farm Labor publication for the first time in 2020.